Problem: Simplify. Rewrite the expression in the form $y^n$. $\left(y^4\right)^{2}=$
$\begin{aligned} \left(y^4\right)^{2}&=y^{4\cdot 2} \\\\ &=y^{8} \end{aligned}$ This follows from the general rule $\left(x^m\right)^{n}=x^{m\cdot n}$. We can also see this is correct by expanding the powers. $\begin{aligned} \left(y^4\right)^{2}&=\underbrace{y^4\cdot y^4}_\text{2 times} \\\\\\ &=\underbrace{ \underbrace{y\cdot y\cdot y\cdot y}_\text{4 times} \cdot \underbrace{y\cdot y\cdot y\cdot y}_\text{4 times}} _\text{2 times} \\\\ &=y^{8} \end{aligned}$ In conclusion, $\left(y^4\right)^{2}=y^{8}$.